There is something horribly seductive and even a little disorientating – a dab of raw jet-lag rubbed straight into the gums – about watching night-time southern hemisphere cricket. Propped up in your frozen armchair, lulled by the watery glow of the streetlights outside, it is easy to feel yourself being sucked in by that powerfully throbbing rectangle in the corner of the room, alive with the bleached-out greens and yellows of the southern summer, finding yourself some time in the wee hours reaching out a hand towards that pulsing blob of light and murmuring "It's … beautiful", transformed into an armchair cricket equivalent of the face-melting Nazis at the end of Raiders of the Lost Ark.

If there is perhaps a little additional magnetism missing from England's current night-time excursions, some colour to go with the almost alarming blue-green fecundity of New Zealand itself, this can perhaps be put down to the absence of one man in particular. England are playing Tests abroad without Graeme Swann for the first time since 2008. And from this side of the world it seems possible they might soon miss him a little more than it is currently fashionable to admit.

To date, Swann's absence for remedial surgery on his elbow injury has been stoically soft-pedalled. The view seems to be that this is, after all, only New Zealand, land of fast-medium hobbits and nuggetty middle-order dwarves. Plus, we have Monty now, who has undoubtedly benefited a little from the second-string spinner's routine of being picked only in flattering conditions, leaping out of the support car to streak along with the leading group on the downhill stretch while remaining cloistered in his trailer during the marathon climbs.

Frankly, though, it isn't quite the same. Swann will be 34 next week and the looming prospect – these things often happen very quickly – of his permanent absence is already an issue around this England team. How many more Tests can we really expect beyond – with any luck – that imminent Ashes double-header? Perhaps while his absence simply nibbles at the fringes it is the right moment to appreciate Swann a little more before he becomes something else, a Swann-shaped hole, a vacancy, a burden for those to come.

Mainly because he is on the face of it so beautifully irreplaceable. England's recent Test match No1 team was on the whole a case of familiar talent brilliantly managed. There will be other Ian Bells, other Stuart Broads: English cricket has always produced these players. What is different now is how thrummingly well conditioned they are. Only Swann and Kevin Pietersen – not just runs! Fast, swiping, power-runs! – present something we might not expect to see again that soon.

With Swann this comes in two parts. First he has just been uncommonly good. You already know this, but let us rehearse the figures. Of his 50 Tests, England have won 25, in which winning causes Swann himself has taken 10 five-fors. In his personal wonder years, 2008-2010, he took 113 Test wickets at 26.55. A Test debutant aged 28 he has become England's defining off-spinner of the modern era, able to attack or defend, contain or destroy, to dismiss with both rip and bluff. Plus there is the paradox of his glorious orthodoxy as a bowler. Elsewhere, finger-spin has become a poutingly sexed-up business, a mille-feuille of intermingled variations, from the zinging, waddling, slingshot conjury of Saeed Ajmal to the princely, short‑form poker player Sunil Narine. Swann, though, is something else, a bowler who, for all his dad-rock hipster slouch, is essentially old-fashioned, his method diligently refined over many years in county cricket.

Back in those early days Swann's action was a whirl of rotating arms and legs, leaping into his delivery stride with the air of a man energetically repelling an airborne squirrel assault. These days he still seems at the point of release to be on the verge of performing a display of air kung fu, but now it is all of a piece, every muscle – his ankles, earlobes, fingernails – joined in a single effort to make the ball fizz from off to leg.

Beyond this perhaps it is simply the fact of Swann's Englishness that stands out. There is hardly a grand tradition here. Left-arm spinners may have traditionally been tolerated as tame eccentrics, from Phil Edmonds, who throughout his Test career seemed somehow always to be bowling in brogues at a picnic, to the early enthusiasms of Zany Monty. But English off-spinners, with obvious resounding exceptions, have generally been an apologetic bunch, a lineage of rather awkward-seeming men, grudgingly wheeled out overseas like an ill-fitting pair of long shorts. Among the most successful, John Emburey, doyen of England's fallow years, was a puzzling figure to the schoolboy observer, this arch-looking endomorphic gentleman with his languidly raised right arm, his 35 consecutive maidens, a tectonic tactician who even now, two decades down the line, may still for all we know be engaged in very slowly and carefully drawing Mohammad Azharuddin – currently on 2,565 not out – ever more marginally out of his crease with a series of imperceptibly risky biannual leg-side dabs.

Perhaps Emburey's greatest gift to English spin bowling is Swann himself, who emerged under his wing at Northamptonshire.

The story of this early, hot-headed Swann is a familiar one. A key member of the team of rock and roll tyros who won the Under-19 World Cup in 1998, his career stuttered after a falling-out with Duncan Fletcher over, among other things, arriving late for the England team bus in South Africa in 2000. After which came the long years of service with Nottinghamshire and Northants – 58,678 career deliveries to date – that would spawn the glorious, late-career bloom.

And 13 years from that false start in Bloemfontein, another Swann-paradox presents itself. Cast out from international cricket on the grounds of being a bad tourist, he has in fact turned out to be one of England's greatest. Of his 14 Test match five-fors, 10 have come abroad, testament to the rare fact that here is an English cricketer – and this is not always the case – who is respected equally around the world. Not to mention a player who might at one stage have gone on to represent the worst of English cricket – pampered, brattish, wasted – but who has through a triumph of heart and sporting intelligence come to represent thevery best.